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Robust stability for stochastic Hopfield neural networks with time delays. (English) Zbl 1122.34065
The Hopfield neural network is described by a stochastic delay differential equation of the form \[ dx(t)=(-Ax(t)+W l(x(t-h)))dt+(Cx(t)+Dx(t-h))dw(t). \] Here \(A,W,C,D\) are matrices with certain properties, \(l\) is a Lipschitz continuous neuron activity function and \(w\) is a Brownian motion. It is shown that certain explicit matrix inequalities imply that the equilibrium solution is robustly, globally, asymptotically stable in the mean-square sense.

MSC:
34K50 Stochastic functional-differential equations
34K20 Stability theory of functional-differential equations
93D09 Robust stability
92B20 Neural networks for/in biological studies, artificial life and related topics
Software:
LMI toolbox
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References:
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